{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Statistics - The Challenger Disaster"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This ipynotebook is an excerpt of the excellent 'Bayesian Methods for Hackers'. For the whole book, check out http://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/.\n",
    "\n",
    "Note that this Notebook requires the package *pymc*.\n",
    "\n",
    "author: Thomas Haslwanter, date: Oct-2015\n",
    "\n",
    "On January 28, 1986, the twenty-fifth flight of the U.S. space shuttle program ended in disaster when one of the rocket boosters of the Shuttle Challenger exploded shortly after lift-off, killing all seven crew members. The presidential commission on the accident concluded that it was caused by the failure of an O-ring in a field joint on the rocket booster, and that this failure was due to a faulty design that made the O-ring unacceptably sensitive to a number of factors including outside temperature. Of the previous 24 flights, data were available on failures of O-rings on 23, (one was lost at sea), and these data were discussed on the evening preceding the Challenger launch, but unfortunately only the data corresponding to the 7 flights on which there was a damage incident were considered important and these were thought to show no obvious trend. The data are shown below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Temp (F), O-Ring failure?\n",
      "[[ 66.   0.]\n",
      " [ 70.   1.]\n",
      " [ 69.   0.]\n",
      " [ 68.   0.]\n",
      " [ 67.   0.]\n",
      " [ 72.   0.]\n",
      " [ 73.   0.]\n",
      " [ 70.   0.]\n",
      " [ 57.   1.]\n",
      " [ 63.   1.]\n",
      " [ 70.   1.]\n",
      " [ 78.   0.]\n",
      " [ 67.   0.]\n",
      " [ 53.   1.]\n",
      " [ 67.   0.]\n",
      " [ 75.   0.]\n",
      " [ 70.   0.]\n",
      " [ 81.   0.]\n",
      " [ 76.   0.]\n",
      " [ 79.   0.]\n",
      " [ 75.   1.]\n",
      " [ 76.   0.]\n",
      " [ 58.   1.]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import os\n",
    "import seaborn as sns\n",
    "from urllib.request import urlopen\n",
    "\n",
    "url_base = 'https://raw.githubusercontent.com/thomas-haslwanter/statsintro_python/master/ipynb/Data/data_bayes/'\n",
    "inFile = 'challenger_data.csv'\n",
    "url = url_base + inFile\n",
    "challenger_data = np.genfromtxt(urlopen(url), skip_header=1, usecols=[1, 2],\n",
    "                                missing_values='NA', delimiter=',')\n",
    "# drop the NA values\n",
    "challenger_data = challenger_data[~np.isnan(challenger_data[:, 1])]\n",
    "\n",
    "# plot it, as a function of tempature (the first column)\n",
    "print(\"Temp (F), O-Ring failure?\")\n",
    "print(challenger_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xe3dad0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEZCAYAAACQK04eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3XlAzPnjP/Dn1Ey1Qq6IUizrCGupiJyRMyrraBF2123d\nq0LudcceYbH2x+5iKdfa68M617EKu1asIx+SJgpbpKSZ5vX7o2/vT6cp20zNvp+PvzTzPp7v1/vd\ns/e83zNDIYQQICIi2TAr6wBERGRcLH4iIplh8RMRyQyLn4hIZlj8REQyw+InIpIZ2RW/Wq2Gs7Mz\n/Pz84Ofnh/79++Ptt9/GgQMHijX/mTNn4OnpiUGDBiEzM7PE6z958iQ+++yzEs9XGJ1OhwkTJqBX\nr17YsWNHnueio6OxYMECAEBUVBT69ev3j9e3b98+DBgwAL6+vujXrx/mzZuHZ8+e/ePl/hO3b9/G\nuHHj4OPjg/79+yMgIAAXL14EkL2vW7VqVeJl5t5Hz549w8iRI6XnmjRpgpSUlBIv89tvv4WPjw+8\nvb3Rr18/BAUF4f79+0VOP3v2bHTq1CnPcerl5YUtW7YAAJKSkvDOO++UOIcxxcfHY8qUKWUdo9jy\n7+t/M2VZBygLVlZW2L9/v/RzQkICRo0aBWtra3h5eb103h9//BGDBw/G+PHjX2nd0dHRePr06SvN\nm9+DBw9w9uxZXLp0CQqFIs9zMTExSExMLJX1ANm5N2zYgP3796NSpUoQQmDhwoVYuHAhQkNDS209\nJTVlyhRMnz4d3bp1AwBcuHAB48ePx9GjRwGgwLgUR+59lJKSgujoaOm5V1neypUrcfPmTWzevBm1\natUCABw4cABDhgxBRESE9Fh+7777Lt59913p5/v376NPnz7o1q0b6tevj2+//bbEWYxJrVbjzp07\nZR2j2PLv638zWRZ/fnXq1MGUKVOwZcsWeHl5QaPRIDQ0FOfPn4dOp0PTpk0xd+5c7N69G0ePHoWV\nlRVSU1Mxa9YsbNy4EYcPH4YQAvb29liwYAFsbW3x6NEjLFiwALdv34a5uTmGDBmCli1bYteuXdDp\ndKhYsSKGDx+OoKAgJCcnAwA6d+6MqVOnFsh34cIFrF69GhkZGVCpVJg6dSpat26NMWPGQKvVYsCA\nAfjss89Qt25dANl/EMLCwvDs2TPMmTMHvr6+SEtLw4wZM3D79m1kZmZiyZIlcHFxKXRbQ0JCYG1t\nnSfDw4cPIYRAeno6KlWqBIVCgalTp+LWrVsAgHXr1iEmJgaPHj3Co0eP4OzsjI8++gjW1tY4fvw4\nNm3aBK1Wi7///hs+Pj7Sdu7Zswfbtm2Dubk5qlatihUrVsDOzg7Hjx/H559/Dq1WCysrKwQGBuKt\nt94qMDYPHz5Eenq69LOrqys++eQTmJllv5jNysrCggULEB0djdTUVAQGBsLLywvr1q1DSkoKQkJC\npPwpKSno379/nn30+++/IyMjA35+fti7dy9yf95xz5492LlzJwCgSpUqCAkJweuvv54nX2JiInbt\n2oVTp06hYsWK0uO+vr7466+/sHnzZsybN684h6n0CsHa2hpqtRre3t74448/sG7dOqjVaiQlJSEh\nIQHVq1fHxx9/DFtbW1y+fBmLFi2CVqtF3bp1kZCQgNmzZ6NZs2aYPXs24uLioFAo0Lx5cyxevDjP\n+s6cOYMVK1bg+++/BwCkpqaiW7duOHr0KL7//nvs3r0bFhYWsLS0xKJFi9CgQQNpXp1Oh3nz5iEp\nKQmjR4/Gli1b8Pvvv2PNmjV4/vw5zMzMMHnyZHTu3Bn79+/HoUOH8OLFC6jVatSuXRvDhg3D9u3b\ncffuXbz77rsYNWoU9u/fjx9++AFCCCQmJsLOzg4rVqyAra0tnj17hqVLl+LmzZvQarVo164dAgMD\nYWZmhhYtWqBbt264ceMGQkNDce3aNYSHh0Or1SIlJQVjx46Fv78/5syZk2dfOzs749y5c6hSpQqA\n7Fd7586dw82bN7F06VK89tpryMjIQEREBE6dOoWNGzfqPV7LDSEz8fHxolWrVgUej4mJEW+99ZYQ\nQoiwsDCxatUq6bm1a9eKhQsXCiGECA4OFv/v//0/IYQQ+/fvF9OnTxdZWVlCCCF2794txowZI4QQ\nYtKkSWL16tVCCCFSU1OFt7e3iIuLE2FhYWLJkiVCCCHWr18vFixYIIQQIj09XcyYMUOkpqbmyZWc\nnCzat28vLl++LOVs27atiI+PL3JbhBBi3759Yty4cUIIISIjI0WzZs2kZWzdulWMGjVKCCHEunXr\nitzW3DQajZg5c6ZwdnYWfn5+YvHixeLEiRPS82FhYaJLly7i8ePHQgghZsyYIVauXCmEEGLEiBHi\n7t27QgghEhMThbOzs0hOThbXrl0T7u7u4sGDB0IIIb766iuxYMECERsbK7y9vUVKSoq0zR4eHuL5\n8+cFcv3444/Czc1NdOzYUUydOlVs375dmi8+Pl40btxY/PLLL0IIIX755Rfh5eUl5c3ZD/l/zv3v\n/GPcuHFjkZycLKKiosSwYcNERkaGEEKI06dPiz59+hTId+jQITFw4MACjwshxLFjx4SPj0+hzwUH\nB4uOHTsKX19f0b17d9G2bVsxadIkERUVVSBXWFiY8PLyEmlpaUIIIcaPHy/CwsKEVqsVnTt3FqdO\nnRJCCHHu3DnRtGlTERUVJQ4cOCBGjx4thBAiKytLzJs3T8TFxRXI0a1bN3HlyhUhhBA7d+4UgYGB\nIisrSzRv3lw8fPhQCCHEd999J8LDwwvMGxkZKby9vYUQQjx58kT07NlTqNVqIUT2cdC5c2dx//59\nsW/fPuHm5iYdB3379hVTp04VQghx7do18eabbwohso/pVq1aScdSaGiomDJlihBCiNmzZ4vt27dL\n2zNr1iyxZcsWIUT2Pjt48KAQQoi0tDQxZMgQ6Ri5dOmSNI7593WTJk1EcnJygZ8jIyOFs7OzuH//\nvhBClOh4LS94xv9/FAoFXnvtNQDZ13hTU1Nx5swZAIBWq0X16tULzHPixAlER0djwIABALLPcl68\neAEA+O233xAUFAQAqFixonTWlFvHjh0xbtw4JCQkoH379pg5c2aes0IA+PPPP+Hk5IQWLVoAABo2\nbIjWrVsjKioKbdq0Kfb21a1bV1pG06ZNsW/fPmkbirOtSqUSoaGhCAoKQmRkJKKiohAcHIx27dph\n7dq1AIBevXqhWrVqAICBAwdi+fLlCAwMxOeff44TJ07g4MGDuH37NgDg+fPnOHfuHDp27Chd6hgx\nYgQAYOfOnXj06BFGjRolnWErlUrcvXsXjRs3zpOrT58+6N69Oy5evIgLFy5g7969+PzzzxEeHg4A\nsLCwQPfu3QFkn7E9fvy42GNWmJxLPSdOnEBcXBz8/f2ljE+fPsXTp09RuXLlPPNotdpCl5WZmfnS\nS0c5l3oyMjIwbdo0mJmZwdXVtdBp27RpgwoVKgAAnJ2dkZKSgps3b0KhUKBDhw4AgLZt26Jhw4YA\nABcXF3zyyScICAiAh4cHRo4cKb1izO3tt9/G/v370axZM+zbtw9BQUEwMzND7969MWTIEHTp0gUe\nHh567yH98ccfePjwISZNmiSNl5mZGW7cuAEAaNGihXQcODg4wMPDAwDg6OiIzMxMPH/+HADQoUMH\nODo6AgAGDx4MX19fAP/7XYyIiAAAvHjxQnrVl7O9AFChQgVs3LgRx48fx927d3Ht2jVp2fmJfN9m\nk/tnOzs72NnZAch+ZVTc47W8YPH/n8uXL6NRo0YAsi8PzJ07Fx07dgSQXVI5hZ6bTqfDmDFj4O/v\nDwDQaDTStWGlMu/Q3rt3D1WrVs3zWIsWLXD06FGcPXsW586dw8CBA7Fhw4Y8LxHzH3w56y2qTIqS\nO49CoZCWW9xt3bt3L6pWrQpPT094e3vD29sbEyZMgKenJ+bPnw8AMDc3z5Pb3Nwcz58/h6+vL3r0\n6AFXV1cMHDgQR48elZ7PXXw5L/V1Ol2ePyhA9uWr/NfCb9++jf3792PmzJlo164d2rVrh8mTJ+O9\n997DoUOH0KNHjyK3OydjDo1GU6Lx1Ol08PHxwcyZM6XHEhMTC5R+y5YtERsbi8ePHxf4gxoZGYlW\nrVrhypUr0iUnhUKR5/4TkH1PatWqVejTpw+2bt2K9957r0AeKyurPNsJZO8PnU6XZ7qcfeTg4IBD\nhw7h/PnzOHfuHEaOHIn58+ejR48eeaYfMGAABgwYgIEDByI1NVX6w7Nq1SrcunULZ8+exRdffIE9\ne/Zgw4YNLx2vhg0bYvfu3dJjSUlJqF69Og4ePAiVSpVn+vw/588PZB+7OT9nZWXh008/lS61paam\n5jm2cv4oJiYmYsiQIRgyZAhcXV3Rs2dPnDx5ssjcOceIRqMpdHk521ac47U8kd27eoCCZXrnzh18\n/vnn0i9Ux44dsWPHDmg0Guh0OsydOzfPTs3RoUMHRERESO9s+eSTTxAYGAgAaN++vXRWnZqailGj\nRiEuLg7m5uZSyaxZswbr169Ht27dMHfuXDRs2BCxsbF51tGyZUvcuXNHuukUExODixcvom3btoVu\nSw5zc/Ni/XEo7raamZlhzZo1eW4Y37lzBw4ODrCxsQEAHD16FM+ePYNOp0N4eDg8PT1x9+5dpKen\nY9q0aejSpQsiIyORmZmJrKwstG3bFmfPnsWjR48AZL/zJTQ0FO3atcOZM2ekVwcnT56Ej49PgT9I\nNWrUQHh4OA4fPiw9lpKSgsePH6NZs2YvHZ9q1arh6tWrAID09HScPn06z9jl7COlUpmnPHOW5+Hh\ngR9//BEPHz4EAOzYsQOjRo0qsJ5atWphxIgRmDFjRp6x27t3Lw4fPowxY8agefPmOHDgAA4cOFCg\n9HNUrlwZQUFBCAsLQ1JSUqHT5NegQQNYWlpK23b58mXExMRAoVDg22+/xezZs+Hh4YGZM2eiY8eO\nuHnzZqH5W7Rogfnz52PQoEEAgOTkZHTp0gVVqlTBiBEjMG3aNOnMPbfcx2DOH8ALFy4AAK5du4ae\nPXsWa1ty78PffvtNmmf37t3w9PQEkP27uG3bNgDZr6QmTJhQ4J1uQPaN+2rVqmHChAnw8PDA8ePH\npXXk39fVq1fHlStXACDPMZafu7t7sY7X8kSWZ/yZmZnw8/MDkH12ZGlpiQ8//BCdOnUCAEycOBGr\nVq2Cn5+fdMMz57JNboMGDUJSUhKGDBkCMzMz1K5dG8uXLwcAzJs3DwsXLkT//v0hhMD48ePh7OyM\nzMxMTJ48GSqVChMmTEBgYCD69esHCwsLNGnSBH379s2zjqpVq+LTTz/FkiVL8Pz5c5ibm2P58uVw\ndHSEWq0u8lJBq1at8Mknn2Dy5MkICAgociyKu61+fn7IyMjAmDFjpLOfevXq4csvv5Qy1KhRA2PH\njkVycjLc3Nwwbtw4qFQqdOnSBb169ULlypXh5OSEhg0bIi4uDh4eHggMDMT7778PhUIBW1tbLFu2\nDLa2tli8eDFmzJgBILtAPv/88zxntUB2GX711VdYs2YNVq5ciQoVKkClUmH06NFo06bNS8enf//+\nOHXqFHr27ImaNWvmedtnzisHlUqFOXPmoGnTpujTpw927twpLa9Dhw4YPXo03nvvPZiZmaFixYpY\nt25doeuaPn069u7di4kTJyIzMxOZmZl48803sXv3btSuXbvIfZNfv379EBERgZUrV0pj8zLm5ub4\n7LPPsGDBAqxduxb16tVDjRo1YGVlBV9fX0RFRaFPnz547bXXYG9vX+RbGQcPHoypU6di48aNALKP\nyYkTJ2LkyJGwtLSESqXC0qVLC8z3xhtvwMzMDIMHD0Z4eDjCwsKwatUqvHjxAkIIrF69uljbn3sf\n2tnZITAwEElJSWjYsCGWLFkCAAgJCcGyZcvQr18/aLVaeHh4YPTo0QXm79ChA/bt24eePXvC2toa\nLVq0QLVq1XD37l04OjpK+/rbb7/F3LlzsWjRIlSuXBkeHh6wtbUtNF/Dhg2LdbyWJwpR1CkRUQnk\nf5cMlQ+rVq3C6NGjUa1aNTx48AA+Pj44evRogXtJpiDn3T85f4Do1cnyjJ9ILnLO5HPudSxdutQk\nS59KF8/4iYhkRpY3d4mI5IzFT0QkM+XqGr9Wm4Xk5HT9E5ZTVatWYP4yYsrZAeYva6ae39a2Uomm\nL1dn/Eqluf6JyjHmLzumnB1g/rJm6vlLqlwVPxERGR6Ln4hIZlj8REQyw+InIpIZFj8Rkcyw+ImI\nZIbFT0QkMyx+IiKZYfETEckMi5+ISGZY/EREMsPiJyKSGRY/EZHMsPiJiGSGxU9EJDMsfiIimWHx\nExHJDIufiEhmWPxERDLD4icikhkWPxGRzLD4iYhkhsVPRCQzLH4iIplRlnWAsqJWx+PGjWsAgMaN\nm8Le3qGME2UrTq7ymr24TD1/abp48QJOnjwGa2tLuLp6wMXFtawjlUjOvrSxqQA7OydZ70tTohBC\niLIOkdvDh6kGXX5GRgYiInYhLu4uVCoVAECj0cDR0QmDBvnDysrqlZdta1vplfMXJ5chs//T/MVR\nXse+LKSkpGDOnEDExt6BSqWEhYUSaWkZqFevPpYtW4UqVaqUdcSXyr8vra0tkZLyrNSORWMzteMn\nP1vbSiWa3uCXev78808EBAQYejXFFhGxCwkJaql4AEClUiEhQY2IiF3lOld5zV5cpp6/NM2ZE4j4\n+DioVP970a1SKREfH4c5cwLLMFnxcF+aNoMW/5YtWxASEgKNRmPI1RSbWh2PuLi7UCgUBZ5TKBSI\ni7sLtTq+XOa6ePFCucxeXOV17MvCxYsXEBt7p8ixiI29g4sXL5RBsuLhvjR9Bi1+JycnrF+/3pCr\nKJEbN67lOUPJT6VSSdeejak4uU6ePFYusxdXeR37spC9L4u+vaZSKXHy5DEjJioZ7kvTZ9Cbu15e\nXlCr1SWap6TXqkrCxqYCrK0t9U7zTzK8yrzFyaVUKqHVmutdzj8dP0ONf3kd+7JgbW0JC4uCv3q5\nH7O2tiy321PUvsz9WGkci8Zmann/iXL3rh5D3mCxs3NCSsqRIs9WNBoN7OycXjnDq94gKk6uXr36\n4j//+dFg2QHD3uAqr2NfFlxdPfDddz/kOeu3sFAiM1MLANBotHB19Si321PYvrS2tkRa2gsApXMs\nGpspHT+FKXc3dwGgvLxxyN7eAY6OToXmEULA0bFs3o5WnFwuLq7lMntxldexLwsuLq6oV69+kWNR\nr179cv22Tu5L02eU4i/sJlBZGTTIH3Xq2Oe54azRaFCnjj0GDfIv17nKa/biMvX8pWnZslVwcHCE\nRqOVHtNotHBwcMSyZavKMFnxcF+aNtm9jz+HIT5EVBovF8vyA1zGerlbXse+LPADXOWDqR4/OUp6\nqUe2xW8I/4aDx1Tzm3J2gPnL2r8hf0nwu3qIiGSGxU9EJDMsfiIimWHxExHJDIufiEhmWPxERDLD\n4icikhkWPxGRzLD4iYhkhsVPRCQzLH4iIplh8RMRyQyLn4hIZlj8REQyw+InIpIZFj8Rkcyw+ImI\nZIbFT0QkMyx+IiKZYfETEckMi5+ISGZY/EREMsPiJyKSGRY/EZHMsPiJiGSGxU9EJDMsfiIimWHx\nExHJDIufiEhmWPxERDLD4icikhkWPxGRzBRZ/Ldu3YKfnx9cXFywdu1aY2YiIiIDKrL4FyxYgAkT\nJuDIkSOIjY1FSEgItFqtMbMREZEBFFn8aWlp6NGjB6pWrYq1a9fCzMwMHTp0wOnTp+Hn52fMjERE\nVIqKLH5LS0tERkYCAJRKJRYvXoyzZ8/C3d0dmzZtMlpAIiIqXUUW//z58zF//nxERET8b2IzMyiV\nStSsWdMo4YiIqPQpi3qiWbNmOHToEP7+++8Cz6nVatjb2xs0GBERGUaRZ/z3799HQkICRowYIf07\nISEB9+7dw/vvv2/MjEREVIqKPOP/7LPPEBkZiaSkJAwbNux/MyiV6NKlizGyERGRARRZ/MuXLwcA\nbN68GWPHjjVaICIiMqwiiz/HkCFDsGPHDqSkpEAIIT3+wQcfGDQYEREZht7inzZtGipVqoQ33ngD\nCoXCGJmIiMiA9Bb/o0ePsHXrVmNkISIiI9D7JW1NmzbF9evXjZGFiIiMQO8Zf0xMDPz8/FC9enVY\nWlpCCAGFQoGjR48aIx8REZUyvcW/bt06Y+QgIiIj0Xupx97eHr///jvCw8NRrVo1nD9/np/aJSIy\nYXqLPzQ0FCdPnsThw4eRlZWFvXv3YsWKFcbIRkREBqC3+E+fPo3Vq1fD0tISFStWxNatW/Hrr78a\nIxsRERmA3uI3M8ueJOc9/JmZmdJjRERkevTe3O3VqxemTZuGJ0+eYNu2bTh48CC8vb2NkY2IiAxA\nb/GPHTsWp06dQp06dXD//n1MnjwZXbt2NUY2IiIygCKL//z589K/rays4Onpmec5Nzc3wyYjIiKD\neOnXMgNASkoK7t27h1atWsHMzAx//PEHGjVqhF27dhktJBERlZ4ii/+bb74BAIwZMwbr1q2Dk5MT\ngOz/fWv+/PnGSUdERKVO79tzEhISpNIHgDp16iAhIcGgoYiIyHD03txt1qwZgoKC0Lt3b+h0Ovzw\nww9wdXU1RjYiIjIAvcX/0UcfYfv27dI1/fbt22Po0KEGD0ZERIZRZPE/fPgQtra2ePToEXr16oVe\nvXpJzyUlJaFOnTpGCUhERKWryOIPCQnBpk2bMHz48Dz/8xa/lpmIyLQVWfybNm0CABw7dgwajQYq\nlQoajQaZmZmwtrY2WkAiIipdet/V8/PPP2PAgAEAgPv376NPnz44cuSIwYMREZFh6C3+DRs2SP/n\nrqOjI/bt24ewsDCDByMiIsPQW/wajQY1atSQfq5evTqEEAYNRUREhqP37ZwuLi6YMWMG+vXrByD7\n0s9bb71l8GBERGQYeot/wYIF+Prrr7F7924olUq4urryffxERCZMb/FbWFjA398fffv2lS7xPHr0\niO/jJyIyUXqLf+PGjdi8eTOqVKkChULB9/ETEZk4vcW/Z88eHDlyBNWqVTNGHiIiMjC97+qpXbs2\nbGxsjJGFiIiMQO8Zf7169TB06FC0bdsWFhYW0uMffPCBQYMREZFh6C3+WrVqoVatWsbIQkRERqC3\n+HlmT0T071Jk8QcEBOT5Vs78vv76a4MEIiIiwyqy+CdPnmzMHEREZCRFFn+bNm2MmYOIiIxE79s5\niYjo34XFT0QkM8Uq/vT0dFy/fh1CCKSnpxs6ExERGZDe4v/tt9/g4+ODiRMn4uHDh/D09MTp06eN\nkY2IiAxAb/GvXbsWO3fuROXKlVGzZk1s374dq1atMkY2IiIyAL3Fr9PpYGtrK/3csGFDgwYiIiLD\n0vvJXTs7Oxw/fhwKhQJPnz7Fjh07+F38REQmTO8Z/+LFi/H999/j/v376N69O65du4bFixcbIxsR\nERmA3jP+6tWrY+3atcbIQkRERqC3+Hv06IGsrCzpZ4VCASsrK7z++usICgqCvb29QQMSEVHp0lv8\nnTp1goODAwYOHAgAOHjwIKKjo+Hp6Ym5c+di27Zths5IRESlSO81/osXL2LUqFGoWLEiKlasiKFD\nh+LGjRvw8vLCkydPjJGRiIhKkd7iNzMzw6lTp6SfT506BQsLCzx69Ahardag4YiIqPTpvdSzfPly\nBAcH48MPPwQAODk5Yfny5di9ezfee+89gwckIqLSpbf4GzVqhH379uHJkycwNzdHxYoVAQCTJk0y\neDgiIip9eov/woUL+PLLL5Geng4hBHQ6HRISEnDs2DFj5CMiolKm9xp/SEgIunfvjqysLAwbNgxO\nTk7o3r27MbIREZEB6C1+KysrvP3222jTpg0qV66Mjz76COfPnzdGNiIiMgC9xW9paYmUlBTUr18f\nf/75JxQKBb+Tn4jIhOkt/lGjRmH69Ono2rUrDhw4gL59+6J58+bGyEZERAag9+Zu79690atXLygU\nCuzbtw+xsbFo2rSpMbIREZEB6C3+27dvIzw8vMCndJcvX26wUEREZDh6i/+DDz5Anz590LhxY2Pk\nISIiA9Nb/JUrV8YHH3xgjCxERGQEeovfz88PH3/8Mdzd3aFU/m9yNzc3gwYjIiLD0Fv8UVFRiI6O\nxu+//y49plAo8PXXXxs0GBERGYbe4r9y5QoOHz5sjCxERGQEet/H36hRI1y/ft0YWYiIyAj0nvHf\nu3cPfn5+sLW1hUqlghACCoUCR48eNUY+IiIqZXqLf/369cbIQURERqK3+G1tbXHy5EmkpaUBALKy\nshAfH4+pU6caPBwREZW+Yn2A6/nz54iLi4OrqyvOnz+Pt956yxjZiIjIAPTe3L1z5w6+/vpreHl5\nYfTo0YiIiEBSUpIxshERkQHoLf7q1atDoVCgfv36uHHjBmrVqoXMzExjZCMiIgPQe6nnjTfewJIl\nS/DOO+/gww8/RFJSEjQajTGyERGRAeg941+4cCF69+6Nhg0bYvLkyUhKSsKaNWuMkY2IiAxA7xn/\nf//7Xzx69AgnTpxAo0aN0K1bN2PkIiIiAymy+B8/fowpU6YgJiYGTk5OUCgUuHPnDlq1aoXQ0FBU\nrlzZmDmJiKiUFHmpZ8mSJXBxccGZM2cQERGB8PBwnDlzBo0bN8ayZcuMmZGIiEpRkcV/48YNzJgx\nAyqVSnrMwsICM2bMwF9//WWUcEREVPqKLH5LS8tCH1coFDAz03tPmIiIyqkiG1yhUBQ508ueIyKi\n8q3Im7sxMTGFvoNHCIGHDx8aNBQRERlOkcV/6NAhY+YgIiIjKbL47e3tjZmDiIiMhHdpiYhkhsVP\nRCQzLH4iIplh8RMRyQyLn4hIZlj8REQyw+InIpIZFj8Rkcyw+ImIZIbFT0QkMyx+IiKZYfETEckM\ni5+ISGZY/EREMsPiJyKSGRY/EZHMsPiJiGSGxU9EJDMsfiIimWHxExHJDIufiEhmWPxERDLD4ici\nkhkWPxGRzLD4iYhkhsVPRCQzLH4iIplRlnUAImNQq+Nx48Y1AEDjxk1hb+9QYJqff/4JP/54AADQ\nt68vevdxd6MCAAATnElEQVTu88rLKu50Fy9ewMmTx2BtbQlXVw+4uLiWfOMMkKuk67SxqQA7O6ci\nl5WznQDQubOnwbfTENtYGssqLxRCCGGohQshsHDhQty4cQMWFhZYunQp6tat+9J5Hj5MNVQcg7O1\nrcT8ZaSo7BkZGYiI2IW4uLtQqVQAAI1GA0dHJwwa5A8rKyskJj7AyJHDkJAQD6Uy+1xIq9WiTh0H\nfPXVDtSqZVfsZRV3upSUFMyZE4jY2DtQqZSwsFAiLS0D9erVx7Jlq1ClSpVib3tp5nrVdVpbWyIl\n5VmBZeXfzux1ag22na+6jYUdP6U5XoZma1upRNMb9FLPkSNHkJmZiV27dmHmzJlYvny5IVdHVEBE\nxC4kJKilX1wAUKlUSEhQIyJiFwBg5MhhePAgQSp9AFAqlXjwIAEjRw4r0bKKO92cOYGIj4+TyjB7\nGiXi4+MwZ05gqW9jSaYrzXUaezvLYhtNkUGL/+LFi+jYsSMAoGXLlrhy5YohV0eUh1odj7i4u1Ao\nFAWeUygUiIu7i+3bv0ZCQjzMzAr+KpiZmSEhIR4///xTsZalVscXa7qff/4JsbF3ipwmNvYOLl68\nUGrbWNxcanV8qa7z4sULRt3OixcvGH0bTZVBi//Zs2eoVOl/L0GUSiV0Op0hV0kkuXHjWp6ztfxU\nKhX27w/Pc6afn1KpxI8/HijWsm7cuFas6X788UCeM+CC0yil6+H6lGaunOvYpbXOkyePGXU7s9dn\n3G00VQa9uVuxYkWkpaVJP+t0ukLPrHIr6bWq8ob5y07+7DY2FWBtbfnSeSwsVDA3f/kxaWVlUaxl\n2dhUAAC901lZWcDCouCvXu7HrK0ti7UvSjOXjU2Ff7TO3I/lTFPYduafp7S2U6lUQqs117ucotaX\n+/Hijqup/r4YtPhbt26N48ePo1evXrh06RIaNWqkdx5TvbkImPbNUcC08xeW3c7OCSkpR4o8c9No\nNOjb1w+rVi0t8qxfq9WiW7c+xVqWnZ0TAOidrlu3PggL+zjP2bCFhRKZmdr/m0YLV1ePYu2L0sxl\nZ+f0yuu0trZEWtqLPMtydbXEd9/9UORZf2lvZ69effGf//z4StuY//gp7riWl9+XcnVz18vLCxYW\nFvD398eKFSswe/ZsQ66OKA97ewc4OjqhsDeuCSHg6OiE4cNHoE4dh0IvQep0OtSp44DevfsUa1n2\n9g7Fmq537z6oV69+kdPUq1e/2G93LM1cxX2bYnGX5eLiatTtdHFxNfo2miqDFr9CocCiRYuwa9cu\n7Nq1C/Xr1zfk6ogKGDTIH3Xq2EOj0UiPaTQa1Kljj0GD/AEAX321A3Z2daDVaqVptFot7Ozq4Kuv\ndpRoWcWdbtmyVXBwcIRGo801jRYODo5YtmxVqW9jSaYrzXUaezvLYhtNkUHfx/8qystLp1dhypdK\nANPOry87P8BV8ulKsk5T/wDXy44fU/gAV0kv9bD4S5EpFydg2vlNOTvA/GXt35C/JPhdPUREMsPi\nJyKSGRY/EZHMsPiJiGSGxU9EJDMsfiIimWHxExHJDIufiEhmWPxERDLD4icikhkWPxGRzLD4iYhk\nhsVPRCQzLH4iIplh8RMRyQyLn4hIZlj8REQyw+InIpIZFj8Rkcyw+ImIZIbFT0QkMyx+IiKZYfET\nEckMi5+ISGZY/EREMsPiJyKSGYUQQpR1CCIiMh6e8RMRyQyLn4hIZlj8REQyw+InIpIZFj8Rkcyw\n+ImIZEZZlisfMGAAKlasCABwcHDA+PHjERwcDDMzM7zxxhtYsGBBWcbTK3/+gIAAjBs3DvXq1QMA\nvPPOO+jdu3cZJiza5s2bcezYMWg0GgwdOhRubm4mNfb58zs7O5vM2O/fvx/79u2DQqHAixcvcP36\ndezYsQPLli0zifEvLP+uXbtMZvy1Wi2CgoKgVquhVCqxZMkSmJubm8TxX1j2jIyMko+9KCMvXrwQ\nfn5+eR4bP368OH/+vBBCiPnz54tffvmlLKIVS2H5w8PDxdatW8smUAlERkaK8ePHCyGESEtLE2Fh\nYSY19oXlN5Wxz2/RokUiPDzcpMY/t5z8pjT+R44cEdOmTRNCCHHmzBkxefJkkxn/wrK/ytiX2aWe\n69evIz09He+//z5GjRqFP//8E3/99RdcXV0BAJ06dcJvv/1WVvH0Kiz/1atXceLECQwfPhxz585F\nenp6Wccs1OnTp9GoUSNMnDgREyZMQJcuXUxq7AvLbypjn1t0dDRu3bqFQYMG4erVqyYz/jny5zeV\n8a9Xrx6ysrIghEBqaiqUSqXJHP/5s6tUKly9ehXHjx8v0diX2aUeKysrvP/++xg0aBBiY2MxZswY\niFwfIra2tkZqampZxdOrsPxjx47F4MGD4ezsjI0bNyIsLAxBQUFlHbWA5ORkJCQkYNOmTbh37x4m\nTJgAnU4nPV/ex76w/OPGjTOJsc9t8+bNmDx5coHHy/v458idv2XLliYz/tbW1oiPj0evXr2QkpKC\njRs34sKFC3meL6/jnz/7pk2bcOfOnRKPfZmd8derVw/9+/eX/l2lShU8fvxYej4tLQ2VK1cuq3h6\nFZa/U6dOcHZ2BgB4eXnh+vXrZRmxSFWqVEHHjh2hVCpRv359WFpa4tmzZ9Lz5X3sC8vfuXNnkxj7\nHKmpqYiNjYWbmxsAwMzsf7+K5X38gYL5u3fvbjLjv23bNnTs2BGHDh3CwYMHERQUBI1GIz1fnse/\nsOyv0jtlVvx79+7FihUrAACJiYl49uwZPDw8EBUVBQD49ddf4eLiUlbx9Cos/8SJE3H58mUAwG+/\n/YZmzZqVZcQiubi44NSpUwCysz9//hzu7u4mM/aF5R83bpxJjH2O8+fPw93dXfq5adOmOH/+PIDy\nP/5Awfzvv/8+oqOjAZT/8bexsZHelFGpUiVotVo4OzubxPGfP7tGo8H48eNLfOyX2Ze0aTQazJ49\nGwkJCTAzM8OsWbNQpUoVhISEQKPRoEGDBvjoo4+gUCjKIp5e+fN/+OGHsLS0xOLFi6FSqWBra4vF\nixfD2tq6rKMWKjQ0FOfOnYMQAjNnzoS9vb3JjD1QMH/VqlVNZuwB4Msvv4RKpcKIESMAALGxsZg3\nb57JjH/+/NeuXTOZ8U9PT8ecOXPw8OFDaLVajBw5Es2aNTOJ47+w7PXr1y/x2PPbOYmIZIYf4CIi\nkhkWPxGRzLD4iYhkhsVPRCQzLH4iIplh8RMRyQyLXwbS09OxePFi9OjRA76+vhg+fHixvovk+PHj\n2LZtW5HPJyUlYdy4cYU+16RJk2Lni4+Px9y5c4s9fVkIDw/HTz/9ZJBl//XXX1izZg0AwNPTE97e\n3vDz84Ovry/8/Pxw5MiRIueNiopCQEBAqWdSq9Xw9PQs0Tzjxo3Dw4cP8+zPxMREBAcHl3o++mfK\n9GuZyTjGjx8PZ2dn/PTTT1Aqlbh27RrGjh2LtWvXSh+5L8zVq1dfutyaNWti06ZNhT5Xkg+/qNVq\n3Lt3r9jTl4U//vgDbdu2Nciyly9fjg0bNgDIHrcvvvgCtWvXLvb8hvqgUUmXm3MsREZGSvuzVq1a\nqFGjBk6ePInOnTuXekZ6NSz+f7moqCjcv38fX3/9tfRY06ZNMWHCBGzYsAFbt25FQEAApkyZAjc3\nN6jVagQEBOCLL77Arl27AAD29vaws7PD6tWrYWZmBhsbG6xZswZpaWkICAjAsWPHoFarMWvWLDx/\n/hxvvvmmtK6cVxsxMTHQ6XQYM2YM+vTpkyfj0qVLER8fjyVLlmDevHnYvHkz/vOf/0Cn06FDhw74\n8MMPoVarMWnSJNStWxc3b95E8+bN0aZNG+zfvx9Pnz7FunXr8Prrr8PT0xPdunXDhQsXoFAosGzZ\nMjRp0gRxcXFYuHAhUlJS8Nprr2HevHlo0qQJZs+ejeTkZNy7dw+zZs1CRkYGtm7dihcvXiAjIwMf\nffQRNBoNjh07hsjISNja2uKHH35A27Zt4evrCyD71c3169exbt06XLp0CQ8ePMCwYcPg4eGRZ50h\nISFo2rRpnm0/d+4catasiUqVKgEAhBB5vjAvx7NnzzB37lwkJiYiKSkJbm5uWLlyJQDg77//xtix\nYxEXF4fXX38dn376KZKSkjB69GhUrVoVVlZW2LJlC1atWoWoqCjodDr4+flh5MiRiIqKwqZNm2Bl\nZYX//ve/aNy4sfTqIyMjAzNnzsTNmzdhY2OD9evXw8bGBqdOncJnn32GrKwsODg4YMmSJbCxsYGn\npye2b99eYH/6+Phg8eLFLP7ypNS+KJrKpS1btkjf353bzZs3hYuLixBCiOHDh4uoqCghhBDx8fHC\n09NTCCFEWFiYCAsLE0IIERAQIKKjo4UQQnzzzTfizJkzeaYdN26c2LNnjxBCiAMHDogmTZoIIYQI\nDQ0V33zzjRBCiNTUVOHt7S3u3buXJ0tkZKQICAgQQgjx66+/iilTpgidTid0Op2YOXOmOHjwoIiP\njxdNmjQR165dE0II4eXlJdauXSvlXL58uRBCiK5du4r169cLIYQ4duyY6NevnxBCCH9/f2neW7du\niZ49ewohhAgODhbBwcFCCCF0Op0YNWqUSE5OFkIIsWfPHul7/4ODg8X+/fsL/FsIIW1rWFiYtB0v\nW2duS5cuFTt37pR+7tq1q+jbt6/w9fUVPj4+Yvr06UIIIX744QexceNGIYQQmZmZwsvLS1y9elVE\nRkaK1q1bC7VaLYQQYuDAgeLEiRPSeCUkJAghhPj222/FihUrhBDZ/5fE8OHDxYULF0RkZKRo1aqV\nSExMlOY/fvy4NH/OPp88ebLYsWOHePz4sfDx8RFPnz4VQgixa9cuMXfuXCm7Wq3Osz9zuLu7S/NQ\n2eMZ/7+cQqFAVlZWgcdzfxthcXTr1g2TJk1C9+7d0a1bN7Rv3x5qtVp6PjIyEmvXrgUA9O/fHyEh\nIQCAs2fP4sWLF9izZw8A4Pnz57h16xYcHBwKXc/Zs2cRHR2NAQMGQAiBFy9ewN7eHq1bt4atra10\n76BWrVrSl4TZ29tLX7AFAIMHDwYAdO3aFcHBwUhMTER0dDRmz54tffV3RkYGnjx5AiD7K4Vzxios\nLAzHjx/HnTt3EBUVBXNz8xKNU86y0tPTi1ynjY2NNP3du3fRrl27PMso7FJP3759cfnyZXz11Vf4\n73//iydPnkjfu96kSRPUqVMHANCgQQMkJycDAKpXry4t5+zZs7hx44Z0b+f58+e4efMmGjRogEaN\nGqFmzZrS/CkpKdIYN2/eHADwxhtvIDk5GZcvX8b9+/cxYsQI6dVJlSpV9I6LnZ0d4uLiyvWXt8kJ\ni/9f7s0338T27duRlZWVp8T++OMPtGjRAkB24eWUk1arLXQ5I0eOhKenJ44fP47Vq1ejV69e8Pb2\nlp5XKBTSJQqFQiF9zbBOp8Pq1aulSxyPHz9+aVHodDqMGDECo0aNApB9icPc3Bx///03VCpVnmmV\nysIP39zbmVNOVlZW2L9/v/R4YmKiVMBWVlYAsst64MCB8PX1hZubGxo3bowdO3YUuo6c8cr/B9TS\n0lLajpetM4dCoSjwx0UU8vVZ33zzDQ4fPgx/f394eHggJiZGmi73/Lmvy+dkyckza9YsdO/eHUD2\n/2lgbW2NS5cuwcLCotD58y9XCIGsrCy4uLhI9yQyMzORlpZWcIDyUSqVeb56msoW98S/nKurKxo2\nbIhly5ZJpX7lyhVs3LgRkyZNAgBUrVoVMTExAIBffvlFmtfc3Fx6tTB48GA8e/YMI0aMwMiRIwvc\n+PXw8MB3330HADh06BAyMzMBAO7u7ti5cyeA7HcB9e/fHwkJCXnmzb0ed3d3HDx4EOnp6dBqtZgw\nYQIOHToEoPBCLEzOu29++eUXvP7666hduzacnJxw8OBBAMCZM2cwfPjwAvPFxsbC3Nwc48ePh7u7\nO3799Vfpj5m5ubk0frnHq6h33FSsWLFY63R0dCwwHoU5e/Ys/P390bdvXwghcP369UJfyeWWe7zc\n3d2xe/duaLVapKWlYejQofjzzz+LPX+Oli1b4tKlS4iNjQUArF+/HqtWrcozTe6xynH//v0iX+WR\n8fGMXwbWrVuHtWvXwtvbG0qlEjY2NggNDZX+q7nRo0cjODgYe/fulc4IAUj/AXuNGjUwY8YMBAcH\nw9zcHK+99hoWLVqUZx0hISEIDAxEeHg4WrRoIX1n+KRJk7Bo0SL069cPOp0OgYGBqFu3bp55GzRo\ngKdPnyIoKAgrV67E9evXMXjwYOh0OnTq1Am+vr5Qq9V5zkZf9o6T33//HREREahQoYJ0A3T16tVY\nsGABtmzZAgsLC3zyyScF5mvSpAmaNGmCnj17okKFCnBzc5NKuX379vj4449RuXJlvPPOO5g+fTp8\nfHzg7u4uXSbJLzQ0FPPnz3/pOrt27Yrdu3fD39//pds1cuRILFy4EF9++SWsra3RunVrxMfHw9HR\nschxyL0sf39/3L17F35+fsjKysLAgQPh5uaW5xLZy+bPUaNGDSxbtgzTpk2DTqeDnZ0dQkND80zf\noEEDpKamSvszJiYGDRo0kG5gU9nj1zLTv0rOO0tyrnmbgqFDh2LDhg3FulZuipYvX4727dvzXT3l\nCC/10L9KefzPM/SZM2cOvvjii7KOYRAPHjzA48ePWfrlDM/4iYhkhmf8REQyw+InIpIZFj8Rkcyw\n+ImIZIbFT0QkMyx+IiKZ+f+zYdsRvMqYnAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x848aeb0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "sns.set_style('darkgrid')\n",
    "np.set_printoptions(precision=3, suppress=True)\n",
    "\n",
    "plt.scatter(challenger_data[:, 0], challenger_data[:, 1], s=75, color=\"k\",\n",
    "            alpha=0.5)\n",
    "plt.yticks([0, 1])\n",
    "plt.ylabel(\"Damage Incident?\")\n",
    "plt.xlabel(\"Outside temperature (Fahrenheit)\")\n",
    "plt.title(\"Defects of the Space Shuttle O-Rings vs temperature\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks clear that the probability of damage incidents occurring increases as the outside temperature decreases. We are interested in modeling the probability here because it does not look like there is a strict cutoff point between temperature and a damage incident occurring. The best we can do is ask \"At temperature t, what is the probability of a damage incident?\". The goal of this example is to answer that question.\n",
    "\n",
    "We need a function of temperature, call it p(t), that is bounded between 0 and 1 (so as to model a probability) and changes from 1 to 0 as we increase temperature. There are actually many such functions, but the most popular choice is the *logistic function*.\n",
    "\n",
    "\n",
    "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t + \\alpha } } $$\n",
    "\n",
    "In this model, the variable $\\beta$ that describes how quickly the function changes from 1 to 0, and $\\alpha$ indicates the location of this change. For example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xee4790>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAECCAYAAAAB2kexAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFXVCCHEjVNQJIcSNUFEnhBA38v8BOv8bOoFeIloAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xdea1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def logistic(x, beta, alpha=0):\n",
    "    return 1.0 / (1.0 + np.exp(np.dot(beta, x) + alpha))\n",
    "\n",
    "x = np.linspace(-4, 4, 100)\n",
    "\n",
    "plt.plot(x, logistic(x, 1), label=r\"$\\beta = 1, \\alpha = 0$\", ls=\"-\", lw=1)\n",
    "plt.plot(x, logistic(x, 3, 6), label=r\"$\\beta = 3, \\alpha = 6$\", ls=\"-\", lw=1)\n",
    "plt.plot(x, logistic(x, -5), label=r\"$\\beta = -5, \\alpha = 0$\", ls=\"--\", lw=1)\n",
    "\n",
    "plt.legend(loc='lower left')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Perform the MCMC-simulations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pymc as pm\n",
    "\n",
    "temperature = challenger_data[:, 0]\n",
    "D = challenger_data[:, 1]  # defect or not?\n",
    "\n",
    "# Define the prior distributions for alpha and beta\n",
    "# 'value' sets the start parameter for the simulation\n",
    "# The second parameter for the normal distributions is the \"precision\",\n",
    "# i.e. the inverse of the standard deviation\n",
    "\n",
    "# notice the`value` here. We explain why below.\n",
    "beta = pm.Normal(\"beta\", 0, 0.001, value=0)\n",
    "alpha = pm.Normal(\"alpha\", 0, 0.001, value=0)\n",
    "\n",
    "\n",
    "@pm.deterministic\n",
    "def p(t=temperature, alpha=alpha, beta=beta):\n",
    "    return 1.0 / (1. + np.exp(beta * t + alpha))\n",
    "\n",
    "# connect the probabilities in `p` with our observations through a\n",
    "# Bernoulli random variable.\n",
    "observed = pm.Bernoulli(\"bernoulli_obs\", p, value=D, observed=True)\n",
    "\n",
    "# Combine the values to a model\n",
    "model = pm.Model([observed, beta, alpha])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 120000 of 120000 complete in 11.0 sec"
     ]
    }
   ],
   "source": [
    "# Perform the simulations\n",
    "map_ = pm.MAP(model)\n",
    "map_.fit()\n",
    "mcmc = pm.MCMC(model)\n",
    "mcmc.sample(120000, 100000, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Show the resulting posterior distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x9611410>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEMCAYAAADDMN02AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nuDYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x95c0230>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha_samples = mcmc.trace('alpha')[:, None]  # best to make them 1d\n",
    "beta_samples = mcmc.trace('beta')[:, None]\n",
    "\n",
    "# histogram of the samples:\n",
    "plt.subplot(211)\n",
    "plt.title(r\"Posterior distributions of the variables $\\alpha, \\beta$\")\n",
    "plt.hist(beta_samples, histtype='stepfilled', bins=35, alpha=0.85,\n",
    "         label=r\"posterior of $\\beta$\", color=\"#7A68A6\", normed=True)\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(212)\n",
    "plt.hist(alpha_samples, histtype='stepfilled', bins=35, alpha=0.85,\n",
    "         label=r\"posterior of $\\alpha$\", color=\"#A60628\", normed=True)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Show the probability curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x9769ef0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAusAAAEZCAYAAAAuS2uyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x976dfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Draw the probability as a function of time\n",
    "t = np.linspace(temperature.min() - 5, temperature.max() + 5, 50)[:, None]\n",
    "p_t = logistic(t.T, beta_samples, alpha_samples)\n",
    "\n",
    "mean_prob_t = p_t.mean(axis=0)\n",
    "\n",
    "plt.figure(figsize=(12.5, 4))\n",
    "\n",
    "plt.plot(t, mean_prob_t, lw=3, label=\"average posterior \\nprobability \\\n",
    "of defect\")\n",
    "plt.plot(t, p_t[0, :], ls=\"--\", label=\"realization from posterior\")\n",
    "plt.plot(t, p_t[-2, :], ls=\"--\", label=\"realization from posterior\")\n",
    "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n",
    "plt.title(\"Posterior expected value of probability of defect; \\\n",
    "plus realizations\")\n",
    "plt.legend(loc=\"lower left\")\n",
    "plt.ylim(-0.1, 1.1)\n",
    "plt.xlim(t.min(), t.max())\n",
    "plt.ylabel(\"probability\")\n",
    "plt.xlabel(\"temperature\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Draw Confidence-Intervals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x97e1f90>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAEhCAYAAACZRRzKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9747830>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats.mstats import mquantiles\n",
    "\n",
    "# vectorized bottom and top 2.5% quantiles for \"confidence interval\"\n",
    "qs = mquantiles(p_t, [0.025, 0.975], axis=0)\n",
    "plt.fill_between(t[:, 0], *qs, alpha=0.7,\n",
    "                 color=\"#7A68A6\")\n",
    "\n",
    "plt.plot(t[:, 0], qs[0], label=\"95% CI\", color=\"#7A68A6\", alpha=0.7)\n",
    "\n",
    "plt.plot(t, mean_prob_t, lw=1, ls=\"--\", color=\"k\",\n",
    "         label=\"average posterior \\nprobability of defect\")\n",
    "\n",
    "plt.xlim(t.min(), t.max())\n",
    "plt.ylim(-0.02, 1.02)\n",
    "plt.legend(loc=\"lower left\")\n",
    "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n",
    "plt.xlabel(\"temp, $t$\")\n",
    "\n",
    "plt.ylabel(\"probability estimate\")\n",
    "plt.title(\"Posterior probability estimates given temp. $t$\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
